As \(\textnormal {rk}\,G >1\) , Margulis' superrigidity
theorem applies to the lattice \(\Gamma \)  of \(G\) : it implies in particular
that \( H^1(\Gamma , \textnormal {Ad}\,\circ \rho ) =0\)  (see
[1]}). Hence the representation \(\rho : \Gamma \longrightarrow {\rm \bf GL}(V)\)  is cohomologically rigid.
